Tuesday, February 18, 2014

Explaining theories to Mom

In my field there is indeed a problem with abstruseness, with the many academics who never even try to put their thoughts in plain language...[The problem is] not that laypeople don’t understand what the academics are saying. It is, instead, that the academics themselves don’t understand what they’re saying.

Don’t get me wrong: I like mathematical modeling. Mathematical modeling is a friend of mine. Math can be a powerful clarifying tool...

But it’s really important to step away from the math and drop the jargon every once in a while, and not just as a public service. Trying to explain what you’re doing intuitively isn’t just for the proles; it’s an important way to check on yourself, to be sure that your story is at least halfway plausible...

I once talked to a theorist...who said that his criterion for serious economics was stuff that you can’t explain to your mother. I would say that if you can’t explain it to your mother, or at least to your non-economist friends, there’s a good chance that you yourself don’t really know what you’re doing.

Math is good. Sometimes jargon is good, too. But plain language and simple intuition are important to keep you grounded.

My first reaction to this was "No way." Think of something like quantum mechanics. You can try to explain that to your mother, and it's going to go something like this: "Look, mom, an electron is both a particle and a wave. The wave sort of represents where you might think you found a particle. But after you find a particle, the wave instantly collapses and then starts expanding out again."

Got that?

Well, that explanation sounds simple, but it won't help Mom judge whether quantum mechanics is a good model or not, or understand anything about how it could be used. In fact, nobody really understands quantum mechanics, but we use it because it works. We tolerate the abstruseness of physics papers because that abstruseness is necessary to get a model that gives good quantitative predictions. In math, we tolerate abstruseness too - if you think quantum mechanics is hard, think of trying to explain number theory to your mom - because it "works" in the ways we want it to work.

There are branches of econ that work this way too. Explaining a Vickrey auction to your mom, or a random-utility discrete choice model, could possibly be very tough (depending on the mom), but there's no denying that these theories are extremely useful in their most technical forms, so we don't worry too much about their abstruseness. This is probably what Albert Einstein meant when he (allegedly) said: "Everything should be made as simple as possible, but no simpler."

What Krugman is implicitly arguing is that macroeconomics is different. The idea seems to be that since academic macro theory is not (yet) good for making quantitative predictions, we should focus more on communicating ideas. Communicating ideas - or "storytelling", as some call it - requires simplicity and clarity. Actually, that idea would not be too different from things Steve Williamson has said:

The problem is that any macroeconomic model is going to be wrong on some dimensions. To be useful, a model must be simple, and simplification makes it wrong in some sense. Subjected to standard econometric tests, it will be rejected. Models that are rejected by the data can nevertheless be extremely useful. I think that point is now widely recognized, and you won't find strong objections to it, as you might have in 1982.

Storytelling - communicating an idea about one mechanism that might be at work in the economy - is a far more modest goal than quantitative prediction. But that doesn't mean it's worthless.

I think the thing that Krugman is complaining about - and that Williamson would probably have less of a problem with - is models that lie somewhere between the intuitive and the quantitatively predictive. In a lot of DSGE-type models, you put in your assumptions, crank them through a set of generally accepted techniques, and come out with an intelligible story...but the intuition for how the machinery produces that story is not always clear or simple.

On one hand, there seems to be no obvious reason why we should avoid making this kind of model, if we have enough time to poke it, play with it, and explore more about how it's getting the results it gets. But if we have to communicate our ideas very quickly, then models this complex can become more of a hindrance than a help. Some people who work for central banks have mentioned to me that in 2008-9, the unwieldiness of their modern DSGE-type macro models made it hard to communicate out-of-the-box thinking and unconventional policy suggestions. In that type of crisis situation, your colleague may be no better equipped to understand you than Mom.

Updates

Some more quotes from popular old physics types:

"You know, I couldn't do it. I couldn't reduce it to the freshman level. That means we really don't understand it."
- Feynman

"Hell, if I could explain it to the average person, it wouldn't have been worth the Nobel prize."
- Feynman

"You do not really understand something unless you can explain it to your grandmother."
- Einstein

"Never express yourself more clearly than you are able to think."
- Bohr

Well many physicists spend a lot of time explaining complex physics to people's mothers. Brian Greene's work on rotational symmetry of calabi-yau manifolds is about as mathematically abstract as you can get--almost ricci-flat in 11 spatial dimensions!--yet he's always on Nova programs and writing popular press books to explain this stuff through story telling.

But Greene doesn't actually talk about *his* work on PBS. Most of it is very vague string theory stuff on the order of matter is made of particles and particles are made of strings. He mentions Calab-Yau manifolds, but they seem more like a totem or religious icon than a particular solution to generalized Einstein's equations. They're a way spacetime can be 11 dimensional while having only 3 extended spatial dimensions and still be effectively flat (approximately zero cosmological constant). But this isn't really mentioned ... so there really isn't any point to discussing Calabi-Yau manifolds at all!

Since this is an economics blog, here's an economics analogy: it's like Noah having a show on PBS where he mentions Calvo pricing without talking about why nominal rigidity is necessary.

All good economists are able to view a subject from a mathematical-technical and an economic-intuitive perspective. It is not just Krugman who first had a hunch, modeled it and saw that his intuition was correct, Stiglitz also works like this.These aren't low level reseachers but Nobel prize laureates who have done ground-breaking TECHNICAL work in several areas.

What differentiates these intellectual giants from guys like Williamson is that the latter might be able to do maths but totally lacks economic understanding. In macro understanding is even more important than technique as many issues are fuzzy and as there are ample of paradoxes. Many good technical economists out there who simply do not /want to) understand something like the paradox of thrift.

Or take comparative advantage, fairly easy on a technical level but explaining it to a laymen is incredibly hard. Nothing against Samuelson "technification" of economics, many earlier brilliant economic writers were often too vague on issues on which you could be more precise. But we overdid it a bit with the rigidity provided by mathematics during the last decades at the cost of losing economic understanding.

First, because it's nowhere near as good or as solid. I mean, yeah, some physics is out there but we know how to build bridges that don't collapse. So we suffer by comparing results.

Second, people who wouldn't dream of commenting on engineers and architects' work (let alone theoretical physicists') feel free to do so on economics coz, you know, they have a job (or not), they earn some money (or not) and they spend it too. Or save it. That makes them experts.

But, the above not withstanding, I agree with Krugman more than with you. Especially on Macro. Macro is political economy. Political economy is A LOT about what we humans do at the polity level and that means most humans can have insights and intuition about it.

When explaining quantum mechanics to your mother, start with a problem that necessitated quantum mechanics. Then explain how they couldn't understand how the result came about. Then explain the insight that quantum mechanics supplied that allowed them to solve the problem.

My 14-old son could get a decent intuition for some basic concept of qm, just by thinking through the consequences of the double-slit experiment. Reality is simpler than you think, just harder to understand.

I believe in the possibility of enlightening grandmothers, although certainly something is lost in the explanation. But the possibility of understanding must not be confused with being interested in the explanation. It will still be hard. Possible but hard. Anyway, I don't think using jargon as "the collapse of the wavepacket" can be considered a simple explanation. It's still jargon, appealing to a precise definition and meaning that is beyond a simple grandmother-approved explanation of the phenomena

Come to Paris (France) and drag your Mom along to the "Palais de la Découverte" (it's near the Champs élysées, so that should'nt be a problem): there is a light diffraction experimental setup available to the public (you actually move the slits across the laser beam) so you can show her the problem, and talk to her about quantum physics afterwards.

Comparing economics to physical science only works when you assume that both disciplines are being used to explain phenomena that 1)exists in the material word and 2) are separable from human actions.

This is demonstrably false for macroeconomics. You are trying to figure out what happens in a system made up of human beings. Decisions are being made by Homo Sapiens Sapiens, not Homo Economicus. If you as an economist can't explain to a human being why human beings are doing what you think humans beings are doing and in your model why, its probably likely that you don't in fact know what you are talking about.

I think queueing theory is a counterexample here. Internet traffic and telephone calls are fairly well described by models without caring about the content of those communications, i.e. why people are communicating.

But supply and demand diagrams are the equivalent of assuming you don't know anything about human behavior:

Forget explaining it to your mother. The question is can it explain it to yourself. A paradox? No. In my field, there's lots of fancy math and much less understanding of it. I know lots of top notch mathematicians who just have no clue what they are doing. The easiest check to see it is to ask somebody to translate the math/models into operational decisions. Specifically, in my field is to ask how differently would you put the trade on and where would you expect then money to come from. It's a dead giveway if somebody cannot explain how the model makes money. On the other hand, if you can see through the math to the source of the edge is a skill worth its weight (literally) in gold.

Einstein's grandmother was lucky that he worked in theoretical physics. At the bottom of physics we assume that there are a limited set of object types with simple mathematical properties arising in a medium with a fairly simple mathematical topology (albeit not completely cracked yet.) In physics this appears to be a good assumption, made for grandmothers perhaps. There's no general reason why grandmothers must be able to understand everything or even anything. It has been said that if the human brain were simple enough to understand we wouldn't be able to understand it. A similar too-many-parts capacity limitation applies to understanding other complex systems.

In economics, the "objects" are wild simplifications of composites of composites of composites. We aren't clear even what their key properties are. To make matters worse, often the objects in question don't exist at all. I see what Krugman is getting at is that when a story is repeated often enough, its narrative objects takes on the psychological property of truth. We all live in a world of hallucinated objects and objects with hallucinated properties. Presumably a number of these are valid simplifications, but we need to check them out. Economic things like financial friction etc obviously don't really exist, they are some kind of the net effect of the specific individual actions of numerous people that make the models work. To make matters worse still, perhaps terminal, the simplifications are regularly chosen to fit ideological frames rather than any evidence base. That's why the grandmother test needs to be applied: She might not get the total picture but she's more likely to spot the hallucinations than someone who has normalized them by repetition.

Current thinking is that human discourse evolved mainly as a means of grooming and controlling others with perhaps a few other useful side effects like intergenerational memory. It certainly didn't evolve as a mechanism to discover the nature of the observable world. That is a retrofit; our working conceit is that it is fit for this purpose. Alternate Krugman: "Humility please!"

Mark Thoma reminded us some time ago of something Alfred Marshall once wrote:

"[I had] a growing feeling in the later years of my work at the subject that a good mathematical theorem dealing with economic hypotheses was very unlikely to be good economics: and I went more and more on the rules - (1) Use mathematics as a shorthand language, rather than an engine of inquiry. (2) Keep to them till you have done. (3) Translate into English. (4) Then illustrate by examples that are important in real life. (5) Burn the mathematics. (6) If you can't succeed in (4), burn (3). This last I did often."

Actually, of course, I think the problem is more complicated than the Marshall quote suggests. Mathematical modeling is hugely important in clarifying our thought. But the key is then to see what that modeling tells you to expect about human behavior--and why. The shortcoming to mathematical modeling is that the economy is (I would suggest) more complicated than we can handle with modeling, and thus the models are always incomplete. I suspect (even in micro, to say nothing of macro) simulations will continue to become more and more important.

Regarding economics there are big ideas that are easy to explain to Mom or Grandma, and ones that are not. In the latter Samuelson himself pointed to comparative advantage, although there are some well-known stories that sort of make sense to Moms and Grandmas, such as how the best secretary in town might want to hire someone else to do their secretarial work if they are just a whole lot better at inventing software than anybody else, or whatever. Some examples that really are not all that easy to explain to Mom or Grandma are some of the more esoteric stuff out of game theory.

However, we also have sort of an opposite problem. Some of the Big Ideas that have won people trips to shake royal hands in Stockholm seem just plain obvious to Mom or Grandma, such as bounded rationality or public choice. Of course people don't know everything and of course people running government agencies are out to maximize their budgets and workforces. Everybody knows that!

But sometimes what is "obvious" to "everybody" is something that economists have ruled out by making their special assumptions. And we know that once economists get hooked on their special assumptions and get into building lots of models based on those assumptions, particularly ones that are not all that easy to explain to Mom or Grandma, they can dismiss as simple-minded those who assert the idea that "everybody knows." Indeed, the Nobels to both Herbert Simon and James Buchanan were ridiculed by others in the profession because they were viewed as somehow not being "good economics." They made respectable, or tried to, ways of thinking in economics that had been rejected by economists, but that "everybody knows."

In any case, when someone gets a Nobel for one of those, the public is often mystified. "Why did they give him a prize for that? It is obvious." But then, OTOH, they are not all that happy when say the prize goes to Hurwicz-Maskin-Myerson, and almost nobody can explain what they got it for other than waving hands and saying, "Well, it helps us set up spectrum auctions," which may be how Noah tried to explain quantum mechanics to his mom before she got bored.

Needless to say, some of these issues do show up in macro, where indeed some ideas such as bounded rationality might well be useful, but are being held at arms length by DSGE modelers due to being too commonsensical, with defenses against them looking sillier and sillier as the models that do not use them perform more and more poorly.

I don't think that's right. Models that fail can inspire good ideas and be cannibalized for useful parts. For example, the Sakata model failed to describe the structure of hadrons, but helped lead to the successful quark model:http://en.wikipedia.org/wiki/Shoichi_Sakata

The claim that "all models are wrong" is a kind of jiu jitsu move to distract your opponent. Of course, even QED is wrong at some level. We judge the usefulness of models by how much they get RIGHT; by how much empirically real stuff they explain in a natural way with minimal assumptions. "The earth is flat" is wrong, and "the earth is a sphere" is also wrong. We prefer the latter because it gets a lot more right than the former; it captures reality more effectively, even if it is still wrong. What does today's macro get empirically right that Steve Williamson and so many others find so impressive? That's the key question, to my mind.

BTW, in connection with your point about models being useful for inspiration and for taking useful parts, you might find some interest in an essay I wrote for Nature Physics a few years ago (http://www.nature.com/nphys/journal/v6/n10/full/nphys1809.html) It looks at a series of failed theories of superconductivity, many of which are barely known today, but each of which played an important role in contributing something to the final, culminating success of the BCS theory. It's an illustration of exactly what you say.

"I think the thing that Krugman is complaining about - and that Williamson would probably have less of a problem with - is models that lie somewhere between the intuitive and the quantitatively predictive."

I doubt it. I suspect the thing that Krugman objects to - and that Williamson is fine with - is models that get important things *exactly* backwards. Like The Great Vacation or high interest rates producing high inflation.I.e. Krugman's problem isn't that it's hard to tell the RBC story in words (it's pretty easy actually); it's that when you *do* put it in words, the words are obviously bullcrap. Williamson (apparently) seriously believes that Volcker caused the great inflation. It would be funny if this stuff wasn't actually important.

If you're confident in your model, then you can use it without understanding it. There are two reasons you might be confident in a model: either you're confident in the underlying assumptions, or the model is reliably confirmed by empirical evidence in an array of contexts broad enough to include the context in which you want to apply the model. But in macroeconomics, neither of these conditions is ever going to be satisfied. You have to understand what's going on in the model in order to know under what conditions it will stop working. This is kind of a generalization of the Lucas critique, and I think the Lucasians end up being hoist on their own petard.

That's a very good point, but the situation is even worse. The necessary conditions pretty much never obtain for any complex systems: be it in physics, medicine, Econ or finance. Just try predicting earthquakes.

If you don't understand a (enough complex) model, it will be really difficult to apply it correctly. That's probably one main source of noise in the economics blogosphere probably because people accept models they don't understand for ideologic reasons...

Understanding a complex model is very different from understanding the underlying DGP. You can know the model in and out and yet understand nothing about the empirical process you are supposed to model. Very popular error in quant finance. Stephen Williamson is a perfect example of that confusion in econ blogosphere.

Re: Wave Particle DualityMy little pea brain says the problem is we don't have a measurement system that tells us what the electron is and encompasses the wave and particle measurements. Yes my brain is that small.

I think Krugman didn't go far enough. I think the heuristic explanation of why the model gives the result it does is often the useful product of the whole effort. One use of models is to clarify thought. The clearer thought is the heuristic explanation of what drove the model. Even if the details of the model aren't true, that informal story can be true. I add that I think that this is the only way in which economic theory has ever been useful.

I think Williamson is trying to convince himself to fall for a very elementary logical error. The fact that it is not true that models which are rejected by the data are necessarily useless doesn't mean that they are useful. I wasn't an economist in 1982, but by 1985 the argument that models were false by definition and could still be useful wasn't controversial. Furthermore, it has been an absolutely standard argument made by economists at least for well over a century. I think he set up a straw man. I am often very irritated by economists' use of made up intellectual history. If it matters enough to mention, it matters enough to get right.

Also I'm trying to get to a clear statement of a sense I have about a catch 22 use of hypothesis testing. The point is that the argument that rejection of a model doesn't tell us anything interesting because it could still be useful is not followed by any discussion of anything which might tell us that it is useless. You note the argument that it doesn't matter if the models are not useful for forecasting, because they are for something else.

I think an effort to see if the world looks roughly like the model is not going to be taken seriously at all, because it involves statistics whose distribution under the null is not known. I think that economic theory defends itself by arguing that hypothesis tests are irrelevant and also that anything which isn't a hypothesis test is invalid econometrics.

I guess I have two questions for straw orthodox macroeconomist . I will make them narrow.1) do you think it is conceivable that the Euler equation for optimal intertemporal consumption choices is no good -- not useful -- something else should be used in macroeconomics ?2) If the answer to question 1 is yes, what would convince you that this conceivable possibility is the case ?

I don't think that he will argue that we know a priori that good models must contain such an Euler equation. I don't think anything could possible convince him that a model without such an Euler equation is better than a model with such an Euler equation.

I think that he has, and incorrectly denies that he has, absolute a priori faith.

Emanuel Derman and Paul Wilmott were concerned with this problem in the context of models used in the financial markets - notably CDOs. In January 2009 they published "The Financial Modellers' Manifesto" http://www.wilmott.com/blogs/eman/index.cfm/2009/1/8/The-Financial-Modelers-Manifesto

with notably "the modellers' Hippocratic oath". It's a good starting point for debate.

My view is that models don't have to be intuitive to start with, but if you think about them long and hard, then they become intuitive - that's when they are readsy for publication.

The Modelers' Hippocratic Oath

~ I will remember that I didn't make the world, and it doesn't satisfy my equations.

~ Though I will use models boldly to estimate value, I will not be overly impressed by mathematics.

~ I will never sacrifice reality for elegance without explaining why I have done so.

~ Nor will I give the people who use my model false comfort about its accuracy. Instead, I will make explicit its assumptions and oversights.

~ I understand that my work may have enormous effects on society and the economy, many of them beyond my comprehension.

I have earned my living applying operations research to real world problems and if I cant translate the intuition behind a counter intuitive result from a mixed-integer staff scheduling problem that I ask my client to implement, then I wont have a job Monday morning. Feels like the bar should be similar for people making policy recommendations that affect us all.

If the topic is important enough to explain to your mother it should justify the effort to translate into plain English. To a non-economist (like myself), Kevin Murphy's wonderful explanation of how to think about the effect of stimulus was very illuminating (he comes up ~17 min into the presentaiton: http://bit.ly/1fdQhzY). Similarly Krugman's explanation and Jim Hamilton's skepticism about manipulation in the crude markets was fantastic.

I am sure several of my students share the same thoughts, judging by their unwillingness to spend time and effort struggling with the concepts. Indeed, they expect the instructor to summarize complex phenomena in simple stories that must be short and entertaining enough to deal with their short attention spans. It is a miracle the financial crisis did not happen sooner, with so many simple-minded folks engaged in such complex transactions. Thanks for encouraging the further dummification of American society. God forbid we ask people to take some time off watching football or following Derek Jeter's saga and educate themselves on a topic that, as you say, is important enough. And then we wonder why Silicon Valley jobs are taken by Indian immigrants while Americans are competing over low-paying jobs at Wall-Mart.

I can't help noticing that Drs. Krugman, Feyman, Einstein, Smith, and even Bohr did not enjoy explaining things to random humanoids but to mothers, and not just mothers but the yiddishe mommeh subtype. The YM types have a strong cultural imperative to turn their sons into successful intellects. They do this by giving glowing looks of admiration while whispering, "Such a Chohim!" Tatte meantime is sitting there thinking that the kid will never earn a penny. Mom turns out to be right causing the above listed series of aphorisms.

I once heard that one of the old great Greek intellects, maybe Aristotle, said the better you understand something (intuitively, I believe) the better you can teach it.

I think this is very true (1) Predominantly with intuitive understanding, not more rote, mechanical, repetitive understanding -- even though the latter kind of understanding can still be very good for applying, producing, even advancing, which kind of surprised me as I advanced in life. (2) All other things equal, which often they're very much not, for example someone could have great intuition, but little patience, or little willingness to consider how much, or little, prerequisite knowledge the student or students have, and so on.

That said, I think we underrate the power of a great teacher with great intuition to really make things clear to laypeople pretty quickly -- and without cheating in a nasty way by making it simpler by lying, or making it less true. I mean intuition, clarity, not hard to understand, and still 100% true, and with the most important intuitions.

I've just had too much life experience seeing this again and again, with terrible hard explanation after terrible hard explanation, and then a great explanation (sometimes from me to myself), and I see how horribly gratuitously hard it was made.

That said, to get deep deep into a lot of complication can take a lot of time even with the best teaching.

The idea here is that thinking can get in the way. There is no reason to expect your human brain that evolved to deal with human-scale physics to have an intuitive sense or really any sense at all about quantum degrees of freedom.

(Is this what gets in the way of macroeconomics? We might have a sense of human-scale i.e. microeconomics, but we really shouldn't expect to have a sense for macro. "Shut up and calculate" might be a good mantra.)

I am coming into this discussion a bit late. On reading Steve Williamson's latest, I couldn't quite understand what he was striving to get at. Was it an attempt to storify RBC models for his mother? Was he trying to be tongue-in-cheek, insulting and stupid, all at the same time? (failing on the first, I am afraid).

Nope, he just has appalling reading skills and did not understand Krugman's point about the need to translate an economic model in prose without jargon, not just to explain it to others but also in order to explain it to yourself, and involuntarily ridiculed himself by showing basic RBC in a technical instead of an intuitive fashion.Typical problem of conservative "economists", as their ideological bullshit is wrong they have to be arcane and cannot be plain.

Yeah he is clearly ideological and has little inclination to look at objective data. For example his latest on the Fed's transcripts, praising Lacker(??!) and Plosser, once again, reveals his lack of understanding of how investors and market participants think and position. No one with actual risk on the table listens to them. The Fed can only affect real spending through the wealth effect. The people who really matter at the Fed were/are : Bernanke (through Feb 2014), Yellen, Dudley and Kocherlakota.

If you want to listen to the dissenting stuff, at least listen to Stein.

But naturally, Williamson, has such a profusion of teeth-marks on his foot, missing the obvious is just quotidien.

you write: In fact, nobody really understands quantum mechanics, but we use it because it works.

This might have been true at one point, but today many people understand (non-relativistic) quantum mechanics pretty well. One reason for this is the new perspective of quantum information and quantum computing, which offer many new metaphors and conceptually simple examples for seeing what is going on.

I think the idea that physicists just understand the math but don't have intuition is outdated, but it's an appealing idea that people like to repeat.

The difficulty in explaining it lies not in the fact that no one understands it, but the fact that even basic concepts such as "probability" and "observe" and "state of the system" need to be understood in a new way which has no similarity to anything we ever see outside a physics experiment. So explaining something like entanglement accurately to non-specialists is very difficult.

Two reasons for a clear and understandable macro.First, a big deal of macro is how people make inferences from the aggregate. That can't be complex, by construction.Second, there is economic policy and policy makers that must understand what they are doing and why.Best,Pablo Mira